Harmonic Lasing in X-Ray FELs: Theory and Experiment

Harmonic lasing is a perspective mode of operation of X-ray FEL user facilities that allows to provide brilliant beamsof higher energy photons for user experiments. Another use-ful application of harmonic lasing is so called HarmonicLasing Self-Seeded Free Electron Laser (HLSS FEL) thatallows to improve spectral brightness of these facilities. Inthe past, harmonic lasing has been demonstrated in the FELoscillators in infrared and visible wavelength ranges, but notin high-gain FELs and not at short wavelengths. In this pa-per we report on the first evidence of the harmonic lasingand the first operation of the HLSS FEL at the soft X-rayFEL user facility FLASH in the wavelength range between4.5 nm and 15 nm